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NBER WORKING PAPER SERIES COLLEGE ACCESS, INITIAL COLLEGE CHOICE AND DEGREE COMPLETION Joshua Goodman Michael Hurwitz Jonathan Smith Working Paper 20996 http://www.nber.org/papers/w20996 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 February 2015 This research reflects the views of the authors and not their corresponding institutions. For helpful comments, we thank Kehinde Ajayi, Chris Avery, Raj Chetty, Damon Clark, Gordon Dahl, David Deming, Yingying Dong, Maria Fitzpatrick,Jessica Howell, Joshua Hyman, Larry Katz and Martin West, as well as conference and seminar participants at Harvard, UC-San Diego, UC-Irvine, NBER, SOLE, SREE, AEFP and the College Board. Shelby Lin and Carlos Paez provided excellent research assistance. Joshua Goodman gratefully acknowledges support from the Taubman Center for State and Local Government. All errors are our own. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. At least one co-author has disclosed a financial relationship of potential relevance for this research. Further information is available online at http://www.nber.org/papers/w20996.ack NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2015 by Joshua Goodman, Michael Hurwitz, and Jonathan Smith. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.

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  • NBER WORKING PAPER SERIES

    COLLEGE ACCESS, INITIAL COLLEGE CHOICE AND DEGREE COMPLETION

    Joshua GoodmanMichael HurwitzJonathan Smith

    Working Paper 20996http://www.nber.org/papers/w20996

    NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

    Cambridge, MA 02138February 2015

    This research reflects the views of the authors and not their corresponding institutions. For helpfulcomments, we thank Kehinde Ajayi, Chris Avery, Raj Chetty, Damon Clark, Gordon Dahl, DavidDeming, Yingying Dong, Maria Fitzpatrick,Jessica Howell, Joshua Hyman, Larry Katz and MartinWest, as well as conference and seminar participants at Harvard, UC-San Diego, UC-Irvine, NBER,SOLE, SREE, AEFP and the College Board. Shelby Lin and Carlos Paez provided excellent researchassistance. Joshua Goodman gratefully acknowledges support from the Taubman Center for State andLocal Government. All errors are our own. The views expressed herein are those of the authors anddo not necessarily reflect the views of the National Bureau of Economic Research.

    At least one co-author has disclosed a financial relationship of potential relevance for this research.Further information is available online at http://www.nber.org/papers/w20996.ack

    NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.

    2015 by Joshua Goodman, Michael Hurwitz, and Jonathan Smith. All rights reserved. Short sectionsof text, not to exceed two paragraphs, may be quoted without explicit permission provided that fullcredit, including notice, is given to the source.

  • College Access, Initial College Choice and Degree CompletionJoshua Goodman, Michael Hurwitz, and Jonathan SmithNBER Working Paper No. 20996February 2015JEL No. I2,I23,J24

    ABSTRACT

    The relatively low degree completion rate of U.S. college students has prompted debate over the extentto which the problem is attributable to the students or to their choice of colleges. Estimating the impactof initial college choice is confounded by the non-random nature of college selection. We solve thisselection problem by studying the universe of SAT-takers in the state of Georgia, where minimumSAT scores required for admission to the four-year public college sector generate exogenous variationin initial college choice. Regression discontinuity estimates comparing the relatively low-skilled studentsjust above and below this minimum threshold show that access to this sector increases enrollmentin four-year colleges, largely by diverting students from two-year community colleges. Most importantly,access to four-year public colleges substantially increases bachelors degree completion rates, particularlyfor low-income students. Conditional on a students own academic skill, the institutional completionrate of his initial college explains a large fraction of his own probability of completion. Consistentwith prior research on college quality and the two-year college penalty, these results may explain partof the labor market return to college quality.

    Joshua GoodmanHarvard Kennedy School79 JFK StreetCambridge, MA 02138and [email protected]

    Michael HurwitzCollege Board1919 M Street NWSuite 300Washington, DC [email protected]

    Jonathan SmithCollege Board1919 M Street NWSuite 300Washington, DC [email protected]

  • 2

    1. Introduction

    A report summarizing the recent White House summit on college access declared that:

    Too few low-income students apply to and attend colleges and universities that are

    the best fit for them, resulting in a high level of academic undermatch that is, many

    low-income students choose a college that does not match their academic ability.

    Students who attend selective institutions, which tend to have more resources available

    for student support, have better education outcomes, even after controlling for student

    ability.1

    The last line of that excerpt highlights the current state of knowledge regarding the impact of

    college choice on students educational outcomes. We have clear evidence that students,

    particularly low-income ones, do not attend the highest quality colleges available to them

    (Roderick et al., 2008; Bowen et al., 2009; Dillon and Smith, 2013; Smith et al., 2013). We also

    have clear evidence that low-cost interventions can alter these enrollment patterns, at least for

    high-skilled students (Hoxby and Turner, 2013). We have, however, relatively little causal

    evidence that choosing a college of lower quality than might otherwise be available generates

    longer-run penalties, such as reduced graduation rates or earnings.

    Such evidence matters because of the need to explain recent negative trends in U.S. college

    completion rates. Completion rates among college enrollers are lower now than in the 1970s, due

    in part to low completion rates of students from lower socioeconomic backgrounds (Belley and

    1 White House Summit on College Education (2014, p. 4). Available at: http://www.whitehouse.gov/sites/default/files/docs/increasing_college_opportunity_for_low-income_students_report.pdf

  • 3

    Lochner 2007; Bound et al. 2010; Bailey and Dynarski 2011). Explanations for the trend tend to

    focus either on student-level factors, such as academic skill and financial resources, or

    postsecondary institution-level factors, such as funding or management quality. The non-random

    selection of students into different colleges generally confounds attempts to distinguish the

    influence of these two types of factors. The major empirical challenge is thus to find an

    exogenous source of variation in college choice.

    We do so by exploiting the complexity of the U.S. college application and enrollment

    system, in which the optimal strategy may be particularly unclear for low-skilled or low-income

    students who lack the information and support necessary to navigate the process (Avery and

    Kane, 2004; Dillon and Smith, 2013). Even high-achieving low-income students fail to apply to

    colleges sufficiently selective to match their academic talents (Hoxby and Avery, 2013). We

    explore a previously understudied factor that adds another complication to the college

    application process, namely the use of test score thresholds by colleges during the admissions

    process. Such thresholds are used by public college systems in a number of states, including

    California, Florida and Texas, though often in combination with other factors such as GPA.

    Across the U.S., roughly one in five colleges report using specific scores as a minimum threshold

    for admission (Briggs, 2009).

    We focus on Georgias state university system (GSUS), which publicly announces minimum

    SAT scores to be used for first-year admission. As a result, such thresholds play an important

    role in access to the states public four-year college sector. We also provide corroborating

    evidence from a second set of individual four-year public colleges, which we describe further

    below, whose use of SAT thresholds in the admissions process is not known to the public. We

  • 4

    develop an algorithm to identify this latter group by exploiting our unique dataset, which

    connects the universe of SAT-takers to college enrollment and completion outcomes.

    A regression discontinuity design comparing the relatively low-skilled students just above

    and below the relevant thresholds yields two main findings. First, access to four-year public

    colleges diverts students largely from two-year colleges, though some would have attended other

    four-year colleges or no college at all. Second, enrollment in four-year public colleges instead of

    those alternatives substantially increases bachelors degree completion rates, by about 30

    percentage points, and even more so for low-income students.

    We see this work as contributing to three recent strands of the literature. First, this is the first

    paper in the U.S. context to document the importance of test score thresholds across multiple

    universities, including an entire state public university system. In this sense, our work resembles

    recent research exploiting the Chilean and Colombian national systems of college admissions

    thresholds to estimate the impact of college quality on a variety of labor market and other

    outcomes (Saavedra, 2008; Kaufmann et al., 2012; Hastings et al., 2013; Palau-Navarro et al.

    2014). We also believe that ours is the first use of college using admissions thresholds hidden

    from applicants.

    Second, the sensitivity of college choice to small test score differences suggests that the

    marginal students here do not face a continuum of postsecondary options in terms of cost and

    quality. Such a continuum may not exist because access to four-year colleges necessarily means

    access to a large, implicit and indivisible subsidy provided by public funding of such institutions.

    Some of this sensitivity to small test score differences may, however, stem from the fact that

    students fail to take low cost steps that would widen their enrollment options. In Georgia, for

    example, retaking the SAT might, for some marginal students, raise their scores sufficiently to

  • 5

    grant them access to the four-year public sector. That apparently small costs have

    disproportionate impacts on students college decisions and can, in some cases, be remedied by

    relatively low-cost interventions has been well documented in previous work (Pallais,

    forthcoming; Bettinger et al., 2012; Hoxby and Turner, 2013; Carrell and Sacerdote, 2013;

    Castleman et al., 2014; Smith et al. 2015). We contribute to this literature by documenting a new

    aspect of the college admissions process, a systematic admissions threshold, that affects college

    choice for students whose retesting and application behavior may be suboptimal.

    Third, and perhaps most important, our work adds to the literature on importance of college

    choice and quality to long-run outcomes. Our central estimates are generated by students

    choosing four-year public colleges largely instead of two-year colleges. The substantial

    graduation rate impacts we observe are consistent with the previously documented graduation

    rate penalty associated with choosing a two-year instead of a four-year college (Rouse, 1995;

    Rouse, 1998; Leigh and Gill, 2003; Long and Kurlaender, 2009; Reynolds, 2012). They are also

    consistent with the growing literature showing a consistently strong relationship between four-

    year college quality and graduation rates (Long, 2008; Smith, 2013). We add to this literature a

    new example of a clearly identified mechanism that generates quality differences and subsequent

    graduation rate impacts. This paper focuses on students near the 20th percentile of the skill

    distribution who are quite different from those studied in recent work focusing on the high end of

    the distribution (Hoxby and Turner, 2013). Our results that college quality affects graduation

    rates for students near the low end of the skill distribution can thus be thought of as

    supplementing the evidence in Cohodes and Goodman (2014) that college quality matters for

    high-skilled students graduation rates.

  • 6

    Prior work has also demonstrated that undermatching, in which students choose colleges

    where the average students academic skill is well below their own, is a widespread

    phenomenon. This is particularly true among low-income students and those who are poorly

    informed about the college application process (Dillon and Smith, 2013). The evidence we

    present is inconsistent with recent attempts to argue that college quality and undermatch do not

    affect graduation rates (Bastedo and Flaster, 2014; Heil et al., 2014). We believe this is some of

    the first clear evidence that graduation rates improve when students overmatch by choosing a

    college where the level of academic skill greatly exceeds his or her own. The marginal students

    generating our estimates are, by definition, among the lowest-skilled at their colleges and thus

    not obviously well-matched in a traditional sense to those institutions. They nonetheless appear

    to benefit greatly from having chosen the higher quality college option.

    Finally, we also note that the improved graduation rates generated by access to higher

    quality colleges may explain part of the labor market return to college quality. Such estimated

    returns are present and large in both OLS and propensity score matching specifications (Black

    and Smith, 2004; 2006). Such estimates diminish somewhat when educational attainment is

    included as a control, suggesting that attainment explains part of that relationship. Other recent

    work exploiting admissions thresholds at individual four-year public colleges also find clear

    evidence of large labor market returns to admission into those colleges, both at the high and low

    end of the skill distribution (Hoekstra, 2009; Zimmerman, 2014). Though we do not observe

    labor market outcomes here, ours is the first such paper to observe college outcomes regardless

    of where a given student ultimately enrolled.

    The structure of the paper is as follows. Section 2 describes the data, the context studied

    here, and our regression discontinuity methodology. Section 3 presents summary statistics,

  • 7

    evidence on retesting behavior, and evidence on the validity of our empirical design. Section 4

    describes our enrollment and completion results. Section 5 discusses the implications of those

    results and concludes.

    2. The Data, Context, and Empirical Strategy

    2.1 The Data

    We use student-level data for the graduating high school classes of 2004-07, collected from

    two sources. The first data set, collected and maintained by the College Board (CB), contains

    information on the nearly 1.5 million students each year who take the SAT, a test many four-year

    colleges require for admission. The SAT contains a math and critical reading section, each of

    which is scored on a scale between 200 and 800 for a maximum composite score of 1600.2

    Students may retake the SAT as often as the testing schedule permits, with each test

    administration costing roughly $40 during the time period studied here. Fee waivers are available

    to low-income students taking the exam for the first or second time. Depending on the context,

    we use two versions of students SAT scores, their first scores and their maximum scores. A

    students maximum composite score is defined as the sum of the maximum math and critical

    reading scores earned regardless of whether they were earned on the same test date. Colleges

    frequently rely on this maximum SAT score for admission. The CB data set also identifies

    colleges to which students send official copies of their SAT scores, which serve as good proxies

    for actual college applications (Card & Krueger, 2005; Pallais forthcoming).3 In addition, the

    2 The writing section was introduced in 2005, making the maximum composite score 2400. For consistency across class, and because colleges typically do not rely on the writing section, we focus here only on the math and critical reading sections. 3 When registering for the SAT, the student has the option to send his scores to four colleges for free. Scores may also be sent at a later date for a fee of $11 per score send.

  • 8

    CB data set contains information on student race, gender, parental income and education, and

    high school attended. Self-reported year of high school graduation is used to assign students to

    graduating classes.

    These data are then merged with data from the National Student Clearinghouse (NSC),

    which collects information on the vast majority of students enrolled in U.S. postsecondary

    institutions. In the years and states studied here, the NSC captured somewhere between 90 and

    95 percent of all students enrolled in Title IV institutions, according to Dynarski et al.

    (forthcoming).4 Data from the NSC allow us to track a students postsecondary trajectory

    including enrollment, transfer behavior and degree completion. We focus on the 2004-07 classes

    for whom we can observe six-year graduation rates.

    Measuring college quality across the two- and four-year sectors is difficult because

    traditional data sources such as the Integrated Postsecondary Education Data System (IPEDS)

    lack comparable measures between the two sectors. IPEDS contains average SAT scores of

    incoming students at four-year colleges but does not have any similar measure for two-year

    colleges, which generally do not require students to have taken the SAT. IPEDS is also limited

    by the fact that degree completion rates reported by colleges do not account for the outcomes of

    transfer students, a particularly acute problem for the two-year sector, which is designed in part

    to facilitate transfers to the four-year sector.

    We therefore use the merged CB and NSC data to construct measures of college quality that

    are comparable across these sectors. To measure student quality, we follow Smith and Stange

    (2015) and assign each college the average score of that colleges first-time students on the

    4 See Table 2, where the enrollment coverage rate for Georgia ranges from 89.9% in 2005 to 94.8 in 2011. Other mid-Atlantic and Southeast states look similar. Some of those not captured by NSC may be enrolling in for-profit institutions.

  • 9

    PSAT, a College Board test taken by high school sophomores and juniors, including many who

    do not later take the SAT. We can thus assign each student a measure of the quality of the peers

    to whom he is exposed at his initial college. Those who do not enroll initially are not assigned

    such a value. To measure institutional degree completion rates, we identify all SAT-takers who

    enroll in that college and then compute the fraction of such students who complete a B.A.

    anywhere within six years. This measure has the advantage of being computable for both the

    two- and four-year sectors, as well as including transfer students among those degree recipients.

    For students who do not initially enroll in college, we assign a value of zero to this institutional

    completion rate variable.

    2.2 Context

    The main analysis sample consists of all students residing in the state of Georgia at the time

    of taking the SAT. We focus on Georgia because its Board of Regents has required that SAT-

    takers score at least 430 in critical reading and at least 400 in math in order to be admitted to

    universities within the Georgia state university system (GSUS).5 We describe the set of 18

    universities governed by this requirement in panel A of Table A.1. These consist of three

    research universities, two regional universities, and 13 state universities. Columns 8 and 9 show

    that five of the 18 universities impose higher minimum thresholds than required by the Board of

    Regents, though only two impose substantially higher thresholds. Georgias state and technical

    5 This requirement has been in effect since well before 2004.

  • 10

    colleges, all of which are primarily two-year institutions, impose much lower minimum

    thresholds of 330 in critical reading and 310 in math.6

    The Georgia context is interesting for three reasons. First, the GSUS minimum admissions

    thresholds correspond to roughly the 20th-25th percentile of the distribution of scores among

    Georgia SAT-takers in the years in question. The marginal student here has relatively low

    academic skills and is often choosing between two- and four-year colleges. The prior literature

    on college choice and quality has tended to focus on a much higher point in the skill distribution

    (Cohodes and Goodman, 2014; Hoxby and Turner, 2013). Second, these thresholds apply to all

    students considering four-year public institutions in Georgia. As we show later, over 60% of

    Georgia students near these thresholds who enroll in four-year colleges do so in these GSUS

    institutions. These thresholds thus affect the majority of college options for students in this

    market. Most prior research exploiting admissions thresholds has focused on individual

    institutions, rather than entire postsecondary systems (Hoekstra, 2009; Zimmerman, 2014).

    Third, the public nature of these requirements means that students can, in theory, take the

    thresholds into account when planning their college application process. We explore whether

    students do, in fact, plan around these thresholds. Because the public nature of the thresholds

    may render score-sending behavior endogenous, we define our sample as all students residing in

    the state of Georgia, rather than just students sending scores to GSUS institutions.

    2.3 Empirical Strategy

    6 A few of the GSUS institutions also have small two-year degree programs. In 2012, for example, 1.1% of the undergraduate degrees awarded by GSUS institutions were associates degrees. As such, we assume that enrollment in GSUS institutions is equivalent to enrollment in a four-year degree program.

  • 11

    To eliminate selection bias driven by different types of students making different college

    choices, we exploit the thresholds previously described. We use a regression discontinuity to

    compare a variety of outcomes between students just above and below these thresholds. We

    generate first stage estimates by running local linear regressions of the form:

    (1)

    Here, GSUS indicates the initial enrollment of student i in high school class c in a Georgia four-

    year public college, (within one year of high school graduation. Access is an indicator for

    meeting or exceeding the relevant test score threshold and Distance measures the number of SAT

    points each students score is from the threshold. We control flexibly for time-varying shocks by

    including high school class fixed effects ( ). Because the two sets of students on either side of

    the threshold are nearly identical in terms of academic skill and other characteristics, the

    coefficient of interest, , estimates the causal effect of being above the admissions threshold on

    enrollment in Georgias four-year public sector.

    We then generate instrumental variable estimates of the impact of enrollment in the four-

    year public sector by running regressions of the form:

    (2)

    where GSUS is instrumented by access according to equation 1. Using GSUS as the endogenous

    regressor allows us to capture the full set of marginal students whose enrollment decisions were

  • 12

    altered by the thresholds.7 This implies that we are estimating the impact of enrollment in the

    four-year public sector relative to the full set of forgone alternatives, largely but not solely two-

    year colleges. As a result, we will not be able to perfectly isolate the two-year/four-year tradeoff,

    for example.

    We use three different sets of outcomes Y. The first are measures of enrollment in other

    college sectors, in order to estimate which types of colleges students are forgoing when induced

    into the four-year public sector. The second are the measures of college quality mentioned

    previously, namely student quality and institutional completion rates, in order to estimate how

    enrollment in the four-year public sector changes the quality of ones initial college. The third

    are various measures of students degree completion, in order to estimate the impact of initial

    college choice on completion rates.

    In Georgia, a student must score at least 430 in reading and at least 400 in math. We

    therefore define distance from the threshold as:

    min 430, 400

    This minimum function collapses the two-dimensional threshold into a single dimension, where

    negative values imply a student has missed at least one threshold and zero or positive values

    imply a student has met or exceeded both thresholds. This method of collapsing a multi-

    dimensional boundary into a single dimension is discussed in Reardon and Robinson (2012) and

    7Usingfouryearcollegeenrollmentastheendogenousvariable,forexamplewouldyieldestimatesthatfailedtoaccountfortheempiricallyimportantfactthatthethresholdsshiftsomestudentsbetweenprivateandpublicfouryearcolleges.

  • 13

    has previously been used in papers such as Cohodes and Goodman (2014) and Papay, Murnane,

    and Willet (2014).

    Because Georgias admissions thresholds are publicly known, we define each students

    distance from the threshold using that students first SAT scores. First scores do not suffer from

    any endogeneity driven by potential retaking of SAT in reaction to failing to meet the thresholds.

    We will provide evidence that, though there is endogenous retaking of SAT in reaction to the

    thresholds, the magnitude of that endogeneity is quite small. As such, we also show estimates in

    which distance has been defined by maximum SAT scores, the measure that is actually employed

    by colleges in the admissions process.8 Using maximum scores yields estimates generally

    similar in magnitude but much more precise than those generated by first scores because of a

    clearer first stage relationship between maximum scores and GSUS enrollment.

    We run the local linear regressions above using a rectangular kernel. We present our primary

    estimates for each outcome using a bandwidth of 100 SAT points. This corresponds fairly

    closely to the optimal bandwidths suggested by Imbens and Kalyanaraman (2012), which

    balances the need for precision against the desire to minimize bias generated by fitting straight

    lines to data that may become non-linear far from the threshold. Such optimal bandwidths vary

    by outcome, so fixing the bandwidth across regressions has the advantage of defining a single

    sample clearly. We test the sensitivity our estimates to a number of bandwidths, including the

    Imbens-Kalyanaraman (IK) optimal bandwidth for each outcome. We cluster standard errors by

    discrete distance to the threshold, as suggested by Card and Lee (2008). Clustering instead by

    high school yields very similar standard errors.

    8 See http://www.usg.edu/academic_affairs_handbook/section3/C660 for the GSUS admissions requirements.

  • 14

    Finally, we disaggregate our estimates by income as measured by the average reported

    income of SAT-takers at each students high school. We characterize students by the average

    income at their high schools for two reasons. First, approximately one-third of SAT-takers failed

    to report their income. Using high school average income allows us to assign everyone to an

    income level. Second, the high school-level income measure is likely a better measure of the

    permanent income of the students family, because of both transitory shocks to income and mis-

    reporting by students. We label students as low income if they come from high schools in the

    bottom third of the income distribution within our sample, an income threshold that corresponds

    to roughly $60,000 a year.

    3 Summary Statistics, Retaking Behavior, and Validity of the Research Design

    3.1 Summary Statistics

    Table 1 presents summary statistics for the RD sub-samples examined here, residents of

    Georgia whose first SAT scores fell within 100 points of the threshold, overall and divided by

    high school income. The College Board data provides information on students gender, race,

    parental education and income. Those data also include SAT scores, retakes and score sends. We

    define indicators for students failing to report gender, race or parental education. The National

    Student Clearinghouse data allow us to construct indicators for both on-time college enrollment,

    defined as enrollment within one year of high school graduation, and degree completion within

    six years of high school graduation.

    In the Georgia sample, 17 percent had parents whose highest education was no high school

    diploma, 29 percent had parents whose highest education was a high school diploma, and 43

    percent had a parent with at least a four-year college degree. Slightly less than one-third of the

  • 15

    sample attended high schools with an average family income of less than $59,799 a year. The

    average student in this sample had a first SAT score of 918, had a maximum SAT score of 960,

    took the SAT 1.9 times, and sent scores to 3.6 colleges. 38 percent first enrolled in a GSUS

    college within one year of graduating high school, while 58 percent enrolled in any four-year

    college. This means that two-thirds of the students who enrolled in a four-year college did so in

    the in-state public sector. 23 percent first enrolled in a two-year college. The average six-year

    B.A. completion rate of students initial colleges, including non-enrollers as zeroes, was 41

    percent. Only 37 percent completed a B.A. degree within six years of graduating high school.

    Another eight percent completed A.A. degrees. Compared to the overall sample, the low income

    sub-sample is less white, more black, has less educated parents, lower SAT scores, and lower

    college enrollment and completion rates.

    3.2 Retaking Behavior

    In order for the regression discontinuity design to estimate causal impacts, we need the

    thresholds to provide exogenous sources of variation in eligibility to attend the colleges in

    question. This, in turn, requires that the running variable itself is not subject to manipulation by

    the student, particularly near the threshold. First SAT scores satisfy this condition but maximum

    SAT scores may fail to do so if students retake the test in response to their distance from the

    threshold. This endogenous retaking behavior should be a potential problem only in settings

    where thresholds are publicly known, such as Georgia.

    Figure 1 shows the graphical version of this relationship between retake probability and

    distance from the GSUS threshold. Retake rates rise with SAT score in this part of the score

    distribution and near the threshold roughly 60 percent of students retake the exam. The figure

  • 16

    shows a small but clear discontinuity. Table 2 presents formal estimates of this discontinuity in

    SAT retaking behavior at the GSUS eligibility threshold, running the regression in equation 1

    with SAT retaking measures as outcomes. Here and in many of the tables that follow, panel A

    examines the entire Georgia sample, using the first SAT score distance as the running variable,

    while panels B and C split the sample by income, as previously described. Panel A shows that

    students whose first SAT scores barely meet the eligibility threshold are about three percentage

    points less likely to retake the SAT than those who barely miss the threshold. Put differently,

    missing the threshold increases retaking rates. Though not shown here, this result is robust to a

    variety of bandwidths and does not appear in other SAT-taking states, suggesting that it is driven

    by the GSUS-specific nature of the thresholds.

    In particular, missing the GSUS thresholds initially increases the probability of retaking the

    SAT two or more times. As a result, those on the threshold retake the SAT 0.06 fewer times than

    those just below the threshold. Those who meet the thresholds initially are no less likely to send

    scores to GSUS institutions, implying that students interested in the four-year public sector

    include such colleges in their initial list of score sends. Meeting the thresholds does decrease the

    total number of colleges students send scores to, likely because retakers are given additional free

    score sends. Interestingly, we observe similar threshold-induced SAT retaking for low-income

    and non-low-income students, even though overall levels of retaking are higher for higher

    income students.

    This paper is, to our knowledge, the first to document exam retaking in response to publicly

    known admission thresholds. Prior research on SAT-taking behavior has shown that some

    students retake the SAT in order to achieve round-numbered scores like 1000 or 1100 (Pope and

    Simonsohn, 2011). Others retake the SAT to increase their maximum scores (Vigdor and

  • 17

    Clotfelter, 2003), which are an important factor in an increasingly competitive admissions

    process (Bound et al., 2009). Theoretical models of admissions systems based on maximum SAT

    scores suggest that such systems have the potential to elicit accurate information about student

    ability, particularly when the alternatives to retaking are test preparation services (Leeds, 2012).

    These prior empirical and theoretical works explore retaking behavior when admissions

    processes are private, in that students know only that higher scores increase their odds of

    admission. Given that that the GSUS thresholds have no significance outside of Georgia, we

    interpret our results as clear evidence of demand for access to public four-year colleges.

    Though retaking behavior reacts endogenously to distance from the threshold, the magnitude

    of this endogeneity is not particularly large, as only three percent of students scores are affected

    by this endogenous retaking. Given that 60 percent of students just below the eligibility threshold

    retake the SAT, this implies that only one twentieth of those retakes are endogenous reactions to

    the threshold. The vast majority of SAT retaking has nothing to do with the threshold itself and

    instead is driven by more general admission incentives to achieve higher scores. Though we will

    focus on estimates that use first SAT scores in order to avoid such endogeneity, we supplement

    these with estimates using maximum SAT scores as the running variable, given that the latter

    differ from the former largely for reasons having nothing to do with the thresholds. We provide

    two further pieces of evidence in favor of taking seriously the results from using the maximum

    SAT score as the running variable in the Georgia context. First, we will show that students on

    either side of the threshold, as defined by maximum SAT scores, look relatively similar in terms

    of observable characteristics. Second, we show in robustness checks that controlling for such

    observables, including the number of retakes, has little impact on our estimated coefficients.

  • 18

    3.3 Validity of the Research Design

    Before turning to our main results concerning college enrollment and completion, we first

    perform two checks of the validity of our regression discontinuity design. The key assumption

    underlying the identification strategy is that students on either side of the threshold are similar in

    terms of observable and unobservable characteristics, so that eligibility for admission is the only

    factor that differs between them. We present two tests that suggest this is the case. First, we

    follow the suggestion in McCrary (2008) to check for discontinuities in the density of

    observations, which would suggest that students can substantially manipulate which side of the

    threshold they fall on. Figure 2 graphs the number of observations in each SAT score cell. No

    discontinuity is apparent, a fact confirmed by more formal statistical tests. The overall shape of

    that distribution looks quite similar in other states and is due in part to the way in which the

    College Board translates raw scores into the scaled scores used here.

    Second, we test for balance in observable covariates across the threshold in Table 3, which

    uses first SAT scores to generate the running variable. Each column tests for a discontinuity at

    the threshold in observable covariates such as gender, race, parental education and high school-

    level income. Panel A shows no statistically significant discontinuities in gender, parental

    education or race, with the only statistically significant but small discontinuity in the fraction of

    students classified as low income. Panels B and C similarly show few statistically significant

    discontinuities in covariates. This is unsurprising given students inability to precisely

    manipulate which side of the threshold they initially fall on. Table 3A, which uses maximum

    SAT scores to generate the running variable, does show more statistically significant

    discontinuities, particularly with respect to race, perhaps a function of small differences in

    retaking behavior by student characteristics. We show in later robustness checks that controlling

  • 19

    for these observable covariates in both the first and maximum score specifications does not

    substantially change our point estimates, further evidence that magnitude of any such

    discontinuities is practically insignificant.

    4 College Enrollment and Completion Effects

    4.1 College Enrollment Effects

    We now turn to the question of how the GSUS admissions threshold affects students

    college enrollment decisions. Figure 3 shows graphically the relationship between distance to the

    threshold and the probability of enrolling in one of Georgias four-year public colleges. Panel A,

    which uses the maximum SAT score-based distance measure, shows a clear, large discontinuity,

    with students with SAT scores just at the threshold substantially more likely to enroll in the four-

    year public sector than those just below it. We note here that GSUS enrollment below the

    threshold is non-zero for two reasons. First, students can also gain admission through the ACT

    exam, the SATs primary alternative, taken by roughly 30% of Georgias high school classes of

    2004-07.9 Second, each institution may exempt individual students from these minimum

    thresholds if such students otherwise demonstrate potential for success through interviews,

    portfolios or life experiences.10 Panel B, using the first SAT score-based distance measure,

    shows a clear discontinuity, but one smaller than in panel A because the maximum SAT score is

    the measure actually used by colleges in the admissions process.

    9ThisoverallACTtakingratecomesfromtheACTswebsiteathttp://www.act.org/newsroom/data/.TheCollegeBoarddatadonotallowus,however,tocomputewhatfractionofSATtakersalsotooktheACT.

    10SuchstudentsareconsideredunderapolicyknownasLimitedAdmissionbecauseoflegalcapsonthenumberofstudentseachinstitutionmaygrantsuchexemptionsto.SomeofthesestudentsaregrantedPresidentialExceptionsinwhichcollegepresidentsdeterminetheyareadmissible.Studentsmayalsogainadmissionbyappealinginitialadmissionsdecisionsandsubmittinglettersofsupportfromteachers,counselorsorotherswhocanattesttotheirpotentialforcollegesuccess.

  • 20

    Focusing on first SAT scores, we show the regression-based estimates of this first stage

    discontinuity in column 1 of Table 4. Access to the four-year public sector increases the

    likelihood of on-time enrollment in that sector by four percentage points, an impact that is highly

    statistically significant and does not differ by student income. The minimum SAT thresholds thus

    provide a strong source of exogenous variation in initial college choice. The instrumental

    variable estimates in columns 2-4 show which alternative college options the marginal student

    forgoes in order to enroll in the four-year public sector. 68 percent of such students would

    otherwise have enrolled in a two-year community college, 23 percent would have enrolled in

    another four-year college (private in-state or out-of-state), and 9 percent would not have enrolled

    in any college.

    As a result, for the marginal student, access to the four-year public sector increases the

    probability of enrollment in any four-year college by 77 percentage points, the reduced form

    versions of which are shown graphically in Figure 4. Though the magnitude of this increase in

    four-year college enrollment does not differ by income, the origin of that shift does. No marginal

    non-low income students would have failed to enroll in college in the absence of access to

    GSUS, whereas roughly one-fourth of low income students would have enrolled nowhere. The

    result is that the GSUS treatment here for low income students is being compared to an

    alternative mixture that is half two-year colleges, one-fourth other four-year colleges, and one-

    fourth no college. For non-low income students, those alternatives are three-fourths two-year

    colleges and one-fourth other four-year colleges.

    That fact that so many of the marginal students forgo two-year colleges for four-year

    public colleges implies a substantial change in the quality of the institution attended. As column

    7 shows, conditional on enrolling on time in a two- or four-year college, the marginal student

  • 21

    induced to enroll in GSUS improves the academic quality of his peers by nearly 19 PSAT points,

    which represents roughly a standard deviation in skill. The magnitude of this change in peer

    quality is more than twice as large for low income students as for non-low income students.

    Bolstering our argument that endogenous retaking is too small to substantially bias our

    results, IV estimates based on maximum SAT scores in Table 4A are generally quite similar to

    those based on first SAT scores. Though the first stage impact of exceeding the threshold based

    on maximum scores is a much larger thirteen percentage points, the marginal student still largely

    foregoes two-year colleges, increases four-year college enrollment by 70 percentage points, and

    dramatically improves the academic quality of his peers. Differences by income are apparent but

    muted relative to those generated using first SAT score-based distance as the running variable.

    4.2 College Completion Effects

    Having shown that the GSUS admissions threshold generates large and clear impacts on

    students initial college choices, we turn now toward estimating the impacts of such choices on

    college completion. Figure 5 shows the reduced form graphical version of these estimates. Panel

    A, based on maximum SAT scores, shows a clear discontinuity with students just above the

    threshold more likely to have completed a B.A. within six years than students just below the

    threshold. The discontinuity in Panel B, based on first SAT scores, is less visually apparent.

    Figure 6 limits the sample to low income students and both panels show a clear discontinuity in

    the B.A. completion rate at the threshold.

    We turn to regression estimates of such discontinuities in Table 5. The previous evidence

    suggests that access to and enrollment in the four-year public sector dramatically increases

    college quality as measured by peers academic skill. The first column of Table 5 presents

  • 22

    another piece of evidence on the impact on college quality using institutional completion rates as

    the outcome, constructed as described previously. The estimates suggest that enrolling in the

    four-year public sector increases the average B.A. completion rate of the institution a student

    attends by 41 percentage points. For low income students that increase is 46 percentage points,

    compared to 34 percentage points for non-low income students. Such large differences are driven

    in part by the substantially higher average B.A. completion rates of four-year institutions relative

    to two-year institutions. Control complier means, as suggested by Abadie et al. (2002) and

    Abadie (2003), imply that in the absence of access to the four-year public sector, the average

    complier would have attended a college with a six-year B.A. completion rate of 24 percent.

    Enrollment in the four-year public sector thus nearly triples the completion rate of the institution

    attended by compliers.

    The remaining columns of Table 5 alternate between instrumental variables and OLS

    estimates of the impact of GSUS enrollment on individual students degree completion

    outcomes. Both sets of columns use the specification from equation 2, with the IV estimates

    using GSUS enrollment as predicted by the first stage and the OLS estimates using actual GSUS

    enrollment. The first striking result, in column 2, is that access-induced enrollment in the four-

    year public sector increases the probability of B.A. completion within six years by 32 percentage

    points. This represents a near tripling of the B.A. completion rate, given that 17 percent of

    control compliers finish their B.A. within that timeframe. In short, access to the four-year public

    sector substantially increases B.A. completion rates.

    Four other facts are worth noting. First, the increase in B.A. completion driven in part by

    a shift away from two-year colleges does not decrease A.A. completion rates in any statistically

    significant way, so that overall degree completion rates rise nearly as much as B.A. rates do. This

  • 23

    implies that relatively few of the marginal students here would have completed their A.A.

    degrees if denied access to the four-year sector. Second, across nearly all of the coefficients

    shown here, we cannot reject the equality of instrumental variables and OLS estimates. It may be

    that our controls for academic skill, namely SAT scores, are sufficiently rich as to soak up much

    of the omitted variable bias one might otherwise worry about in the non-quasi-experimental

    estimates, though this appears to be somewhat less true for low income students. Third, as shown

    in panel A, conditional on a students own academic skill, the institutional completion rate of his

    initial college explains a large fraction of his own probability of completion. The impact of

    access-induced enrollment on individual students completion rates is roughly three-fourths the

    magnitude of the impact on institution-level completion rates.

    Fourth, and finally, the estimated impacts on B.A. completions rates appear to be

    substantially larger for low income students than for their higher income peers. For low income

    students, enrollment in the four-year public sector increases B.A. completion by 50 percentage

    points, compared to a control complier mean completion rate of only 2 percent. The comparable

    figure for higher income students is a statistically insignificant 13 percentage point increase in

    B.A. completion, compared to a control complier mean completion rate of 31 percentage points.

    Access to the four-year public sector appears to be much more critical to the B.A. completion of

    low income students than that of higher income students. These magnitudes suggest that,

    conditional on a students own academic skill, the institutional completion rate of his initial

    college explains basically all of a low income students own probability of completion but less

    than half of a higher students probability of completion.

    Table 5A replicates Table 5, using maximum SAT scores as the basis of the running

    variable. Relative to the first SAT score-based specification, these estimates are substantially

  • 24

    more precise, are generally somewhat smaller in magnitude, and vary less by income. Here, four-

    year public enrollment increases the B.A. completion rate by 23 percentage points, with low

    income students seeing a 27 percentage point increase. Though these point estimates are smaller

    than in Table 5, most of the points highlighted above still hold. Associate degree completion

    rates decrease very little, instrumental variables estimates are extremely close in magnitude to

    OLS estimates, and institutional completion rates of initial colleges still explain a large fraction

    of individual completion rates.

    4.3 Robustness Checks and Heterogeneity

    In tables 6 and 6A, we test the robustness of our central estimates to a variety of

    alternative bandwidths and kernels, and to the inclusion of demographic controls. The top row of

    each panel uses the optimal bandwidth for the reduced form suggested by Imbens and

    Kalyanaraman (2012), as well as a triangular kernel.11 Our baseline specification in each panel is

    the row labelled Bandwidth = 100. The overall impression is that, although the first stage

    magnitude is somewhat sensitive to bandwidth, all of the IV estimates of central interest are

    relatively robust to such choices.

    Figure 7 confirms this further, graphing the IV estimate of GSUS enrollment on six-year

    B.A. completion rates against a variety of bandwidths. For the first SAT score-based

    specification in panel B, the estimate is statistically significant and remarkably stable between 30

    and 40 percentage points, with the exception of the very smallest bandwidths shown. For the

    maximum SAT-scored based specification in panel A, the estimate is highly statistically

    11Becausethefirststagesoptimalbandwidthisusuallyslightlysmallerthanthatofthereducedform,weusetheBandwidth=50specificationtoapproximatetheestimateswewouldfindifweinsteadusedthefirststageoptimalbandwidtheverywhere.

  • 25

    significant and always between 20 and 30 percentage points for all of the bandwidths shown. In

    neither set of specifications does the addition of demographic controls substantively change the

    estimated coefficients, suggesting that any imbalance in observable covariates across the

    threshold is too small to be driving our main conclusions.

    Though not shown here, we also run placebo tests measuring the reduced form impact of

    the GSUS thresholds on these outcomes for students in state of North Carolina, where such

    thresholds are irrelevant. Those placebo tests yield point estimates quite close to zero and

    statistically insignificant, suggesting the impact of the GSUS thresholds is specific to Georgia

    and not generated by spurious features of the data.

    In Table 7, we split our sample by gender, race and parental education in order to see

    whether any of the central estimates of interest appear to vary according to such student

    characteristics. We see relatively little evidence of such systematic heterogeneity. In particular,

    the impact of GSUS enrollment on institutional and individual B.A. completion rates is

    remarkably similar across gender, race and parental education groups. This lack of heterogeneity

    may be due to the fact that all of our analyses condition on SAT scores as a measure of academic

    skill. Such scores may be sufficient to capture much of other underlying differences between

    different demographic subgroups of students, thus explaining the lack of heterogeneity we

    observe.

    4.4 Colleges With Hidden Thresholds

    We present one final piece of evidence that we gather from outside of the Georgia

    context. To do so, we construct a second sample from the merged CB-NSC data that consists of

    all students who sent their SAT scores to one of seven colleges we identify as using minimum

  • 26

    test score thresholds in the admissions process, even though the existence of such thresholds is

    not publicly known. We refer to these as hidden threshold colleges. We define hidden

    threshold colleges as those for which students matriculation probabilities as a function of the

    maximum composite SAT show a clear and substantial discontinuity. We now describe the

    algorithm by which we identified these colleges.

    We started with the graduating high school class of 2004 and conducted the following

    procedure. First, we identified all students who sent SAT scores to that college. Second, using

    those students, we employed a regression discontinuity design to test for the presence of

    discontinuities in the probability of matriculation as a function of maximum composite SAT

    scores. To do so, we ran a series of local linear regressions in which we varied the potential

    location of the discontinuity from a composite score of 600 to a composite score of 1400, testing

    all possible values in between. Third, we kept only potential discontinuities where the t-statistic

    on the threshold indicator exceeded three. We also eliminated colleges where the density of score

    senders changed dramatically around potential discontinuities. Colleges that violated this density

    condition were those that made public their specific thresholds, making it much less likely that

    students just above and below the threshold were similar in terms of observable or unobservable

    characteristics. Fourth, to verify that these discontinuities were not anomalies, we then repeated

    this search process for the remaining colleges but for each the subsequent classes of 2005-07,

    keeping only colleges that showed clear discontinuities for all four classes.

    The result of this process was the identification of seven colleges that clearly employ

    minimum SAT thresholds in the admissions process. A few points are worth noting. First, the

    seven colleges fall into two groups, those with low hidden thresholds (composite SAT scores

    ranging from 754-1028) and those with high hidden thresholds (composite SAT scores ranging

  • 27

    from 1192-1216). Figures A.1 and A.2 show the probability that applicants enroll in these

    colleges as a function of applicants distance from the threshold we identify as relevant for their

    high school class. The low threshold colleges have six-year graduation rates in the 40-60 percent

    range, slightly higher than the average GSUS institution. The high threshold colleges have six-

    year graduation rates in the 70-80 percent range, substantially higher than the GSUS and low

    threshold colleges. All seven colleges are located in either the Mid-Atlantic or the Southeast and

    all seven are public, so we further limit the sample to students who are in-state residents.12.

    Second, extensive internet research revealed no public indication of the use of such

    thresholds for any of these seven colleges, strongly implying that these colleges keep this aspect

    of their admission processes hidden from applicants. Because these thresholds are not publicly

    known, score-sending behavior should not be endogenous with respect to those thresholds. We

    confirm this empirically below and thus define our sample to include only those who send scores

    to these colleges, a definition which should not generate any selection bias. Third, the slight

    variation in the location of each colleges threshold over time suggests that colleges may be

    setting these thresholds based either on the percentiles represented by these composite scores or

    based on their capacity to read a fixed number of applications each year.

    We then run nearly identical regressions as in the Georgia context, with only three small

    differences. First, instead of just using high school class fixed effects, we include target college

    by high school class fixed effects. Second, we define each students distance from the threshold

    as:

    12 In addition to being consistent with the Georgia analysis, which uses in-state students, students who send scores from out of state are likely unusual in other respects. Out-of-state students may, for example, meet special admissions criteria, such as those for recruited athletes. We include as multiple observations the relatively few students who send scores to multiple hidden threshold colleges. Excluding these students entirely or limiting each to only a single college has no impact on the results.

  • 28

    where MINSAT is the threshold composite score identified by our algorithm for the applicants

    target college (TC) and class. We use only maximum composite SAT scores when defining

    distance here because the hidden nature of the thresholds precludes endogenous retaking of the

    test, a fact that we confirm empirically but do not show. We also confirm that there is no heaping

    of the distance measure as constructed, nor any covariate imbalance across the threshold. The

    third difference is that we use a bandwidth of 200 SAT points, which is closer to the optimal

    bandwidth suggested by the IK procedure for most of these outcomes.13

    Table 8 shows the results of these regressions, with panel A including applicants to low

    hidden threshold colleges, panels B and C dividing those applicants by income, and panel D

    focusing on applicants to high hidden threshold colleges. The first column shows a very strong

    first stage across all of the panels, with those above the thresholds 10-14 percentage points more

    likely to enroll in their target colleges than those below the thresholds. The strength of the first

    stage is by design, given that we search for colleges in part on the basis of this first stage.

    Access induced enrollment in low hidden threshold colleges diverts 35 percent of marginal

    students from two-year colleges and 57 percent from other four-year colleges, fractions that are

    relatively similar across the two income groups. Compared to students in Georgia who were

    largely diverted from two-year colleges, the marginal student here is largely diverted from

    another four-year college. The net effect of this is that enrollment in the target college increases

    the institutional completion rate of the college attended by 23 percentage points. For the average 13Wealsonotethatabandwidthof200pointsforastudentscompositeSATisequivalenttoabandwidthof100pointsforasinglecomponent,asusedintheGeorgiacontext.

  • 29

    student, individual B.A. completion rates rise by a statistically insignificant 7 percentage points.

    This is driven entirely by a marginally statistically significant 22 percentage point increase in the

    completion rate for low income students. Similar to the Georgia context, it appears that access to

    four-year public colleges has large effects on low income students degree completion rates. For

    higher income applicants to low hidden threshold colleges, this change in initial college choice

    has no clear impact on completion rates. Similarly, there is little impact of initial college choice

    for applicants to high hidden threshold colleges, nearly all of whom would otherwise have

    attended another four-year institution.

    5 Discussion and Conclusion

    We document substantial college enrollment effects generated by the use of test score

    thresholds as part of the admissions process. Exogenous variation in access to four-year colleges

    shifts substantial numbers of students out of the two-year and into the four-year college sector,

    dramatically changing the quality of the institution attended, as measured by the institutions

    own graduation rate. The fact that small differences in test scores can generate such large

    differences in initial college choice is itself remarkable. This suggests that students are not

    applying to a continuum of colleges, either because they are applying too narrowly or because

    such a continuum may not exist in some postsecondary markets. In Georgia, for example, a

    student denied access to the four-year public sector may not have other four-year college options

    available near that point in the price and quality distribution. That enrollment effects are

    observed using first SAT scores in Georgia may also suggest that some students are not retaking

    the SAT sufficiently often in reaction to just missing the admissions threshold.14

    14 We cannot, however, exclude the possibility that students whose first SAT scores place them just below the threshold have private information suggesting retaking the test would be unlikely to improve their scores.

  • 30

    The observed B.A. completion effects suggest that initial college choice matters. Perhaps

    most importantly, our instrumental variables estimates allow us to reject the claim that the

    marginal students here have such low academic skills that they are incapable of completing a

    four-year college degree, a result consistent with nave OLS estimates. That A.A. completion

    rates are not clearly diminished also implies that most of these marginal students would have

    failed to earn their two-year college degrees had they started college in the two-year sector.

    We cannot rule out another margin of impact, namely the importance of unobserved college

    match quality. If missing these thresholds pushes students away from their desired college and to

    another college of similar observed quality, there may still be graduation impacts. If, for

    example, the desired college is closer to home or less expensive than the alternative, this may

    decrease completion rates. In analysis available on request, we show that these thresholds do not

    clearly change the distance between a students home and initial college, suggesting that

    proximity is one form of match quality that cannot explain these completion effects. Though we

    ultimately cannot isolate which margin is driving the B.A. completion results, the overall

    implication is that enrolling in a lower quality institution appears to have meaningful long-run

    consequences.

    In the Georgia context, we see graduation effects across the income distribution, though the

    estimated impacts are larger for low-income students. For applicants to low hidden threshold

    colleges, the graduation effects are entirely concentrated among low-income students. The

    contrast may be due to the fact that the system-wide nature of the Georgia thresholds

    substantially constrains the set of college alternatives available even to non-low-income students,

    whereas applicants to hidden threshold colleges are constrained only with respect to the single

    college using that threshold. That these effects are generally larger for low-income students may

  • 31

    be due to the fact that higher income students diverted into lower quality institutions nonetheless

    have the academic and financial resources to succeed in those institutions. That low-income

    students long-run outcomes are most sensitive to initial college choice seems unsurprising.

    Finally, that applicants to high hidden threshold colleges see little change in their choice of

    college sector and their completion rates is likely due to the fact that such high-achieving

    students are sophisticated college applicants. They apply to a larger number of schools, so that

    failing to gain admission to any single school does not alter their probability of attending a four-

    year college. As such, their enrollment rates are unaffected. The thresholds do, however, affect

    the quality of their four-year college without affecting graduation rates, in contrast to the results

    in Cohodes and Goodman (2014). One crucial distinction is that marginal students here are, by

    definition, at the bottom of the skill distribution at their college, which was not true in the case of

    the merit scholarship program studied by Cohodes and Goodman (2014). If relatively high-

    skilled students benefit from being near the top of their peer group or suffer from being at the

    bottom, this could offset the potentially beneficial graduation impacts of attending a higher

    quality institution.

    Our results have three implications for education policy. First, our findings are consistent

    with the two-year penalty literature (Long and Kurlaender, 2009; Reynolds, 2012; Smith, 2013)

    in that starting at a two-year college may reduce their probability of earning a B.A. degree. This

    is driven both by the fact that two-year college completion and transfer rates are so low and that

    some of the marginal students here, though relatively low-skilled, are nonetheless capable of

    completing their four-year college degrees. Our results imply that concerns about pushing low-

    income students into higher quality colleges, as articulated in Bastedo and Flaster (2014), may be

    ill-founded. Our results suggest that overmatching, or enrolling in a college where one is

  • 32

    substantially less academically skilled than ones peers, is actually beneficial for students, at

    least in terms of degree completion.

    Second, these findings reinforce previous research emphasizing the need for students to make

    test-taking and application choices that do not restrict their available postsecondary options. The

    thresholds studied here are simply one additional factor adding to the importance of such

    choices. In settings where thresholds are publicly known, this implies that students falling below

    those thresholds might be encouraged to retake the relevant exam, either through information

    campaigns or reductions in the costs of retaking. More generally, students should be encouraged

    to expand their college application portfolios in order to improve the quality of the college

    options available to them.

    Third, our estimates suggest one potential unintended consequence of a recent proposal by

    the Obama administration to make community college free for a large portion of the student

    population. Lowering the price of community college may improve college enrollment and

    degree completion for students who would not otherwise have attended college. By changing the

    relative price of the two- and four-year sectors, such a proposal may, however, actually lower

    degree completion rates for students drawn out of the four-year and into the two-year sector. The

    net effect of this proposal thus depends on the number of students on each margin (i.e. between

    two-year and no college and between two-year and four-year college) and the fraction of such

    marginal students whose degree completion is affected by that choice. Our results suggest that

    price reform might need to be accompanied by quality reform, if possible, in order to avoid such

    unintended consequences.

    Finally, further research is needed to determine why initial college choice matters and which

    aspects of college quality are responsible for these graduation effects. Our work provides some

  • 33

    of the clearest evidence to date on the importance of initial college choice for low-skilled

    students and low-income students. The precise mechanism through which this operates warrants

    more work.

  • 34

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    Figure 1: SAT Retaking in Georgia

    Notes: Shown above is the fraction of students retaking the SAT at least once, as a function of the distance of their first SAT scores from the GSUS threshold. The sample consists of the 2004-07 graduating high school classes residing in Georgia the time of taking the SAT.

  • 39

    Figure 2: Density of Running Variable

    Notes: Shown above is the number of students whose first SAT scores place them at a given distance from the GSUS admissions thresholds. The sample consists of the 2004-07 graduating high school classes residing in Georgia the time of taking the SAT.

  • 40

    Figure 3: Enrollment in GSUS Colleges

    (A) Maximum SAT Score

    (B) First SAT Score

    Notes: Shown above is the fraction of students enrolling in a GSUS college within a year of graduating high school, as a function of the distance from the GSUS threshold of their maximum (panel A) or first (panel B) SAT scores. The sample consists of the 2004-07 graduating high school classes residing in Georgia the time of taking the SAT.

    0.1

    .2.3

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    Frac

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    -100 -80 -60 -40 -20 0 20 40 60 80 100Distance From Threshold, Max SAT Score

    .1.2

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    -100 -80 -60 -40 -20 0 20 40 60 80 100Distance From Threshold, First SAT Score

  • 41

    Figure 4: Four-Year College Enrollment

    (A) Maximum SAT Score

    (B) First SAT Score

    Notes: Shown above is the fraction of students enrolling in any four-year college within a year of graduating high school, as a function of the distance from the GSUS threshold of their maximum (panel A) or first (panel B) SAT scores. The sample consists of the 2004-07 graduating high school classes residing in Georgia the time of taking the SAT.

    .2.4

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    -100 -80 -60 -40 -20 0 20 40 60 80 100Distance From Threshold

  • 42

    Figure 5: B.A. Completion

    (A) Maximum SAT Score

    (B) First SAT Score

    Notes: Shown above is the fraction of students completing a B.A. within six years of graduating high school, as a function of the distance from the GSUS threshold of their maximum (panel A) or first (panel B) SAT scores. The sample consists of the 2004-07 graduating high school classes residing in Georgia the time of taking the SAT.

    .1.2

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    -100 -80 -60 -40 -20 0 20 40 60 80 100Distance From Threshold, First SAT

  • 43

    Figure 6: B.A. Completion, Low Income Students

    (A) Maximum SAT Score

    (B) First SAT Score

    Notes: Shown above is the fraction of low income students completing a B.A. within six years of graduating high school, as a function of the distance from the GSUS threshold of their maximum (panel A) or first (panel B) SAT scores. The sample consists of the 2004-07 graduating high school classes residing in Georgia the time of taking the SAT.

    .1.2

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    -100 -80 -60 -40 -20 0 20 40 60 80 100Distance From Threshold, Max SAT

    Low Income High Schools

    .1.2

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    Low Income High Schools

  • 44

    Figure 7: Sensitivity of B.A. Completion Estimate to Bandwidth

    (A) Maximum SAT Score

    (B) First SAT Score

    Notes: Shown above are the point estimates and confidence intervals for estimates of the effect of GSUS enrollment on B.A. completion within six years.

    0

    0.05

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    50 60 70 80 90 100 110 120 130 140 150

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    50 60 70 80 90 100 110 120 130 140 150

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  • 45

    (1) (2) (3)All LowIncome NonLowIncome

    GASATTakers GASATTakers GASATTakers(A)DemographicsMale 0.44 0.40 0.45Female 0.56 0.59 0.55White 0.54 0.35 0.63Black 0.27 0.49 0.17Hispanic 0.03 0.03 0.04Asian 0.04 0.03 0.04Missingrace/ethnicity 0.08 0.07 0.09HighestparentaleducationHSdropout 0.17 0.25 0.13HighestparentaleducationHSgraduate 0.29 0.35 0.27HighestparentaleducationBAorhigher 0.43 0.30 0.49Missingparentaleducation 0.11 0.10 0.12Lowincomehighschool(

  • 46

    (1) (2) (3) (4) (5) (6)Retook Retook Retook Number Sentscore ScoreSAT once 2+times oftakes toGSUS sends

    (A)AllstudentsAccess 0.031*** 0.011 0.021*** 0.061*** 0.023 0.076***

    (0.004) (0.007) (0.005) (0.008) (0.020) (0.024)Meanbelowthreshold 0.599 0.372 0.227 1.906 1.819 3.700N 162,266 162,266 162,266 162,266 162,266 162,266

    (B)LowincomeAccess 0.033*** 0.014 0.019*** 0.057*** 0.007 0.031

    (0.008) (0.011) (0.006) (0.016) (0.028) (0.034)Meanbelowthreshold 0.550 0.363 0.187 1.797 1.977 4.015N 52,007 52,007 52,007 52,007 52,007 52,007

    (C)NonlowincomeAccess 0.034*** 0.009 0.025*** 0.070*** 0.037 0.098***

    (0.005) (0.007) (0.006) (0.010) (0.024) (0.027)Meanbelowthreshold 0.627 0.377 0.249 1.967 1.729 3.522N 110,249 110,249 110,249 110,249 110,249 110,249

    Table2:SATRetakingandScoreSendingBehaviorinGeorgia

    Note: Heteroskedasticity robust standard errors clustered by distance to the admissions thresholdare in parentheses (* p

  • 47

    (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)Parent Parent Parent Missing

    Missing highschoolhighschool B.A. parental LowMale White Black Hispanic Asian race dropout graduate orhigher education income

    (A)AllstudentsAccess 0.005 0.012* 0.012* 0.000 0.002 0.002 0.005 0.001 0.006 0.001 0.013**

    (0.003) (0.006) (0.006) (0.002) (0.002) (0.003) (0.004) (0.005) (0.006) (0.003) (0.005)Meanbelowthreshold 0.422 0.512 0.303 0.034 0.037 0.083 0.178 0.313 0.398 0.111 0.361N 162,266 162,266 162,266 162,266 162,266 162,266 162,266 162,266 162,266 162,266 162,266

    (B)LowincomeAccess 0.001 0.011* 0.008 0.001 0.006** 0.004 0.007 0.006 0.010* 0.004

    (0.007) (0.006) (0.008) (0.003) (0.002) (0.005) (0.005) (0.008) (0.005) (0.007)Meanbelowthreshold 0.391 0.325 0.505 0.033 0.029 0.075 0.243 0.355 0.294 0.107N 52,007 52,007 52,007 52,007 52,007 52,007 52,007 52,007 52,007 52,007

    (C)NonlowincomeAccess 0.009*** 0.002 0.006 0.001 0.001 0.001 0.005 0.000 0.009 0.004

    (0.003) (0.007) (0.006) (0.002) (0.003) (0.003) (0.005) (0.006) (0.007) (0.003)Meanbelowthreshold 0.439 0.618 0.189 0.035 0.042 0.087 0.141 0.289 0.457 0.113N 110,249 110,249 110,249 110,249 110,249 110,249 110,249 110,249 110,249 110,249

    Table3:CovariateBalanceTests

    Note: Heteroskedasticity robust standard errors clustered by distance to the admissions threshold are in parentheses (* p

  • 48

    (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Parent Parent Parent Missing

    Missing highschoolhighschool B.A. parental LowMale Black Hispanic Asian race dropout graduate orhigher education income

    (A)AllstudentsAccess 0.006 0.034*** 0.000 0.001 0.007** 0.003 0.002 0.004 0.004 0.024***

    (0.005) (0.008) (0.002) (0.002) (0.003) (0.005) (0.005) (0.004) (0.004) (0.007)Meanbelowthreshold 0.427 0.373 0.034 0.038 0.084 0.209 0.334 0.346 0.111 0.413N 149,566 149,566 149,566 149,566 149,566 149,566 149,566 149,566 149,566 149,566

    (B)LowincomeAccess 0.006 0.033*** 0.000 0.006* 0.003 0.001 0.005 0.008 0.002

    (0.008) (0.006) (0.003) (0.004) (0.004) (0.006) (0.010) (0.007) (0.007)Meanbelowthreshold 0.397 0.568 0.029 0.028 0.073 0.266 0.356 0.274 0.104N 51,489 51,489 51,489 51,489 51,489 51,489 51,489 51,489 51,489

    (C)NonlowincomeAccess 0.009* 0.019** 0.000 0.002 0.009*** 0.001 0.003 0.004 0.006**

    (0.005) (0.008) (0.003) (0.002) (0.003) (0.006) (0.005) (0.005) (0.003)Meanbelowthreshold 0.448 0.235 0.038 0.046 0.092 0.169 0.319 0.397 0.116N 98,066 98,066 98,066 98,066 98,066 98,066 98,066 98,066 98,066

    Table3A:CovariateBalanceTests

    Note: Heteroskedasticity robust standard errors clustered by distance to the admissions threshold are in parentheses (* p

  • 49

    (1) (2) (3) (4) (5) (6) (7)Enrolled Enrolled Enrolled Didnot Enrolled Ever Medianontime, ontime, ontime, enroll ontime, enrolled, PSATGSUS any nonGSUS ontime any any score,4year 2year 4year atany 4year 4year ontimecollege college college college college college college(FS) (IV) (IV) (IV) (IV) (IV) (IV)

    (A)AllstudentsAccess/EnrolledGSUS 0.040*** 0.684*** 0.227*** 0.089 0.773*** 0.293*** 18.7***

    (0.007) (0.063) (0.072) (0.099) (0.072) (0.055) (4.5)Control(complier)mean 0.345 81.1N 162,266 162,266 162,266 162,266 162,266 162,266 131,137

    (B)LowincomeAccess/EnrolledGSUS 0.045*** 0.493*** 0.241* 0.266*** 0.759*** 0.407*** 28.0***

    (0.007) (0.115) (0.143) (0.093) (0.143) (0.115) (6.7)Control(complier)mean 0.370 77.6N 52,007 52,007 52,007 52,007 52,007 52,007 40,662

    (C)NonlowincomeAccess/EnrolledGSUS 0.040*** 0.779*** 0.234*** 0.013 0.766*** 0.190** 12.0***

    (0.009) (0.117) (0.062) (0.132) (0.062) (0.083) (3.6)Control(complier)mean 0.330 83.1N 110,249 110,249 110,249 110,249 110,249 110,249 90,467

    Table4:InitialCollegeEnrollment

    Note: Heteroskedasticity robust standard errors clustered by distance to the admissions threshold are inparentheses (* p

  • 50

    (1) (2) (3) (4) (5) (6) (7)Enrolled Enrolled Enrolled Didnot Enrolled Ever Medianontime, ontime, ontime, enroll ontime, enrolled, PSATGSUS any nonGSUS ontime any any score,4year 2year 4year atany 4year 4year ontimecollege college college college college college college(First (IV) (IV) (IV) (IV) (IV) (IV)

    (A)AllstudentsAccess/EnrolledGSUS 0.127*** 0.538*** 0.301*** 0.161*** 0.699*** 0.334*** 13.4***

    (0.013) (0.031) (0.019) (0.024) (0.019) (0.017) (0.844)Control(complier)mean 0.235 81.5N 149,566 149,566 149,566 149,566 149,566 149,566 118,546

    (B)LowincomeAccess/EnrolledGSUS 0.128*** 0.428*** 0.352*** 0.220*** 0.648*** 0.304*** 15.4***

    (0.016) (0.052) (0.053) (0.021) (0.053) (0.033) (1.549)Control(complier)mean 0.290 80.2N 51,489 51,489 51,489 51,489 51,489 51,489 39,769

    (C)NonlowincomeAccess/EnrolledGSUS 0.134*** 0.611*** 0.260*** 0.129*** 0.740*** 0.348*** 11.1***